SURFACE AREAS
AND VOLUMES
10 cm
10 cm
10 cm
60 cm
l = ?
What is formula for
CSA of cone ?
What is formula for
CSA of cylinder ?
What is formula for
CSA of hemisphere ?
Q. A toy is combination of a cylinder, hemisphere and a cone,
each with radius 10 cm. Height of the conical part is 10 cm and total
height is 60 cm. Find the total surface area and volume of the toy.
TSA of toy =
CSA of cone +
π r l
?
✔
CSA of cylinder +
CSA of hemisphere
2 π r H
?
✔
2 π r2
✔
H = ?
Q. A toy is combination of a cylinder, hemisphere and a cone,
each with radius 10 cm. Height of the conical part is 10 cm and total
height is 60 cm. Find the total surface area and volume of the toy.
14.1 cm
l
=
∴
=
10
× 1.41
=
2
10
Sol.
10 cm
10 cm
10 cm
60 cm
l = ?
10 cm
l = 14.1cm
40 cm
TSA of toy =
CSA of cone +
π r l
?
Let us find the slant height (l )
What is the formula to find slant height (l )?
Slant height (l )
=
r2
+
h2
=
(10)2
+
(10)2
=
100
+
100
=
200
✔
Height of cylinder =
60 –
10 –
=
10
∴
Height of cylinder
=
40 cm
We know that,
Radius =
Height
In Hemisphere,
Let us find slant height of cone
and height of cylinder
Let us find height
of cylinder
Total height
– height of cone
– height of hemisphere
CSA of cylinder +
CSA of hemisphere
2 π r H
?
✔
2 π r2
H = ?
l =
r2
+
h2
TSA of toy =
CSA of cone +
CSA of cylinder +
CSA of hemisphere
Q. A toy is combination of a cylinder, hemisphere and a cone,
each with radius 10 cm. Height of the conical part is 10 cm and total
height is 60 cm. Find the total surface area and volume of the toy.
TSA of the toy
= CSA of cone
+ CSA of cylinder
+ CSA of hemisphere
Total surface area of toy is 3582.74 cm2
= πrl
+ 2πrH
+ 2πr²
= πr
(l + 2H + 2r)
= 3.14 ×
10
(14.1
l = 14.1cm
r = 10cm
H = 40cm
+ 2
× 40
+ 2
× 10)
= 31.4
(14.1
+ 80
+ 20)
= 31.4
= 3582.74 cm2
∴
× 114.1
10 cm
10 cm
10 cm
60 cm
10 cm
l = 14.1cm
40 cm
Sol.
×
×
π r l
2 π r H
2 π r2